Students develop and employ different cognitive strategies to learn mathematics. Additionally, some students learn better in a competitive learning environment while others learn better in a cooperative environment. Through a series of questions on the PISA student questionnaire, PISA measured the following learning strategies in mathematics and preferences for learning situations.
Learning strategies in mathematics
Memorization/rehearsal is a learning strategy that involves the use of memorization and rehearsing techniques and includes learning key themes and doing repeated learning of materials.
Elaboration is a learning strategy that involves elaborating mathematics concepts beyond the topic at hand such as making connections to related areas and thinking about alternative solutions, etc.
Control is a learning strategy that involves planning, regulating, and monitoring of learning in mathematics.
Preferences for learning situations
Preferences for cooperative learning situations reflect the preference for cooperative learning such as learning in groups.
Preferences for competitive learning situations reflect the preference on striving to be better than others.
Canadian students are more likely to use memorization, elaboration, and control strategies
Compared to the OECD average, Canadian students reported higher levels of using memorization and rehearsing techniques (learning answers and problems off by heart, repeating learning materials, and remembering every step in a mathematics procedure) for learning mathematics (Appendix Table B3.4). There were, however, differences among the provinces (Table 3.3). Compared to the Canadian average, students in Newfoundland and Labrador, and Alberta reported higher levels of memorization and rehearsal strategies, students in Prince Edward Island reported lower levels while students in the other provinces did not differ from the Canadian average (Appendix Table B3.4). However, this does not mean that memorization alone defines or characterizes Canadian and provincial approaches to mathematics.
Compared to the OECD average, Canadian students also reported slightly higher levels of elaborating mathematics concepts beyond the topic at hand such as making connections to related areas and thinking about alternative solutions. At the provincial level, only students in British Columbia differed from the Canadian average by reporting lower levels of elaboration strategies (Appendix Table B3.4).
PISA also explored the extent to which students take control over their learning of mathematics by involving themselves in the planning, regulating and monitoring of their learning in mathematics. However, it should be noted that there might be notable differences in how students from different countries perceive control strategies. For example, the degree to which students report that they are involved in their learning may depend on differences in the culturally-driven expectations of the learning process among different countries.
Compared to the OECD average, Canadian students were more likely to make use of these types of control strategies. There was a great deal of provincial variation in the level of control strategies reported by students (Table 3.3). Compared to the Canadian average, students in Prince Edward Island, Nova Scotia, New Brunswick, Ontario, Manitoba, Saskatchewan, Alberta, and British Columbia reported below-average use of
control strategies. Students in Newfoundland and Labrador and Quebec reported levels above the Canadian average (Appendix Table B3.4).
Canadian students are more likely to prefer both cooperative and competitive learning situations
Learning behaviour can also be influenced by students’
preferences for different kinds of learning situations.
Compared to the OECD average, Canadian students as a whole were more likely to express preferences for both cooperative learning such as learning in groups and competitive learning such as striving to be better than others. It should be noted that preferences for cooperative and competitive learning are not mutually exclusive of each other. Provincial averages did not differ from the Canadian average with the following exceptions: students in Newfoundland and Labrador and New Brunswick reported higher levels of preferences for cooperative learning situations; students in Alberta reported higher levels of preferences for competitive learning situations;
students in Quebec reported lower levels of preferences for cooperative learning; and students in Prince Edward Island and Manitoba reported lower levels of preferences for competitive learning situations (Appendix Table B3.4).
Table 3.3
Provincial average scores on indices of learning strategies and preferences for learning relative to the Canadian average
Provinces performing Provinces performing Provinces performing significantly higher* the same* as the significantly lower* than than the Canadian average Canadian average the Canadian average Memorization/rehearsal Newfoundland and Labrador, Nova Scotia, New Brunswick, Prince Edward Island
Alberta Quebec, Ontario, Manitoba,
Saskatchewan, British Columbia
Elaboration strategies Newfoundland and Labrador, British Columbia
Prince Edward Island, Nova Scotia, New Brunswick, Quebec, Ontario, Manitoba, Saskatchewan, Alberta
Control strategies Newfoundland and Labrador, Prince Edward Island,
Quebec Nova Scotia, New Brunswick,
Ontario, Manitoba, Saskatchewan, Alberta, British Columbia Preferences for Newfoundland and Labrador, Prince Edward Island, Nova Scotia, Quebec
cooperative learning New Brunswick Ontario, Manitoba, Saskatchewan, Alberta, British Columbia
Preferences for Alberta Newfoundland and Labrador, Prince Edward Island,
competitive learning Nova Scotia, New Brunswick, Manitoba
Quebec, Ontario, Saskatchewan, British Columbia
* Differences in scores are statistically significant only when confidence intervals do not overlap. Provinces performing about the same as Canada as a whole have a confidence interval that overlaps that of Canada. Provinces within each cell are ordered from east to west.
Student learning strategies and preferred learning situations are related to mathematics performance
How do learning strategies relate to mathematics performance? Do various learning strategies directly impact performance or do students with different abilities have preferences for different learning strategies? It is difficult to determine whether various learning strategies directly impact performance or whether students with different abilities prefer different learning strategies or are in learning situations where different strategies are encouraged. For example, while it may be that students perform well because of the strategies they use for learning, it may also be the case that teachers tailor learning for individual students by encouraging high-performing students and low-high-performing students to use different learning strategies.
Overall, learning strategies were related to mathematics performance but the difference was not as pronounced as those observed for student engagement (Figure 3.2). Students who exhibited high levels of control strategies (one standard deviation above the average) scored 49 points higher than did students who exhibited low levels (one standard deviation below the average). The use of memorization and rehearsal strategies, as well as elaboration strategies, was also positively related to mathematics achievement. For each of these indices, students who exhibited high levels scored 34 and 43 points higher respectively than students who exhibited low levels.
While preferences for competitive learning situations were positively related to mathematics achievement, preferences for cooperative learning were not significantly related to achievement. Students with high levels of preference for competitive learning situations scored 52 points higher than did students with low levels of preference.
High performers exhibit different learning strategies and preferences for learning situations than low achievers.
Table 3.4 shows the average score on the various indices of learning strategies and preferences for learning situations for high and low performers on the combined mathematics scale21. This table shows that high and low performers in mathematics prefer a different set of learning strategies. Overall, high performers tended to
Figure 3.2
Combined mathematics score for students with high levels of various learning strategies and preferences for learning compared to students with low levels
350 400 450 500 550 650
Average combined mathematics score
350 400 450 500 550 Average combined mathematics score 650
600 600
Preferences for competitve
learning Preferences for
cooperative learning Elaboration
strategies Control strategies
Memorization strategies
Students who are low* on the index Students who are high* on the index
* Students low on a given index are defined as those falling one standard deviation below the mean. Students high on a given index are defined as those falling one standard deviation above the mean.
report higher levels of elaboration and control strategies than low performers. High performers also reported higher preferences for competitive learning environments whereas low performers reported higher preferences for cooperative learning. The same patterns were observed in all provinces with the exception of Quebec. In Quebec, high performers reported lower levels of both memorization strategies and elaboration strategies than low performers (Appendix Table B3.5).
Summary
The results from this chapter show that student engagement in mathematics is related to mathematics achievement. Both provincially and Canada-wide, students with high levels of mathematics confidence performed the equivalent of two proficiency levels higher (133 points) on the combined mathematics scale than did students with low levels. Students with high levels of mathematics anxiety performed the equivalent of one proficiency level lower (71 points) in mathematics than did students with low levels. Motivation to learn mathematics as measured by interest and enjoyment in mathematics and belief in the usefulness of mathematics was also positively related to achievement. It is difficult to disentangle the associations observed between mathematics engagement and performance. For example, are high motivation and confidence and reduced anxiety the causes of strong performance or by-products of doing well in mathematics? Nevertheless, the strong link between student engagement in mathematics and mathematics performance suggest that high motivation and self-confidence and low mathematics anxiety are important outcomes in themselves.
Of particular interest is the finding that even when controlling for ability, girls consistently show much lower interest and enjoyment in mathematics, lower self-related beliefs and higher levels of mathematics anxiety than
Table 3.4
Average score for learning strategies and preferences for learning:
low versus high performers on the combined mathematics scale, Canada
Low performers on the High performers on the
combined mathematics scale combined mathematics scale
Index Standard Index Standard
average error average error
Memorization/rehearsal strategies 0.00 (0.04) 0.24 (0.02)
Control strategies -0.25 (0.04) 0.24 (0.03)
Elaboration strategies 0.09 (0.03) 0.23 (0.02)
Preferences for cooperative learning 0.19 (0.04) -0.02 (0.02)
Preferences for competitive learning 0.09 (0.03) 0.44 (0.03)
Note: Low performers are defined as those who score below 420 points on the combined mathematics scale which corresponds to a proficiency level of one or less. High performers are defined as those who score above 606 points on the combined mathematics scale, which corresponds to a proficiency level of five or higher.
boys. This gender inequity may contribute to gender differences in the educational and occupational career choices.
Learning strategies and preferences for learning were not as strongly related to mathematics performance as was student engagement. However, the results revealed that high and low performers in mathematics had different learning strategies and preferences for learning.
While high performers in mathematics were more likely to prefer memorization/rehearsal, elaboration and control strategies and competitive learning environments, low performers were more likely to prefer cooperative learning environments.
Notes
21 Low performers are defined as those who score below 420 points on the combined mathematics scale which corresponds to a proficiency level of one or less. High performers are defined as those who score above 606 points on the combined mathematics scale which corresponds to a proficiency level of five or higher.